Math Problem Statement

The sum of [6] consecutive even numbers is [270]. What is the second number in this sequence?

Solution

Let's solve this step-by-step.

  1. Let the first even number in the sequence be xx.
  2. Since we have six consecutive even numbers, the sequence will be: x,x+2,x+4,x+6,x+8,x+10x, x + 2, x + 4, x + 6, x + 8, x + 10
  3. The sum of these six numbers is given as 270: x+(x+2)+(x+4)+(x+6)+(x+8)+(x+10)=270x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 270
  4. Simplify the left side: 6x+30=2706x + 30 = 270
  5. Subtract 30 from both sides: 6x=2406x = 240
  6. Divide by 6: x=40x = 40

Now, we know the first number is 4040. The sequence is therefore: 40,42,44,46,48,5040, 42, 44, 46, 48, 50

The second number in this sequence is 42.

Would you like more details, or do you have any questions?

Here are five related questions:

  1. What would the first number be if the sum of six consecutive even numbers were 300?
  2. How do we solve for the sum of six consecutive odd numbers?
  3. Can we find the average of these six numbers, and how does it relate to the middle numbers?
  4. How would the sequence change if we had consecutive odd numbers instead?
  5. What would the second number be if the sequence started with 38 instead of 40?

Tip: When dealing with sequences, set up an equation to simplify the process of finding the terms.

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Sequences

Formulas

Sum of arithmetic sequence
Linear equation

Theorems

Solving linear equations

Suitable Grade Level

Grades 6-8